A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth

Abstract In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than

• Type: Journal
• Year: 2008
• Where: JSCIC
• Authors: Paul Macklin, John Lowengrub
• Keywords: Boundary Conditions, JSCIC 2008, Nonlinear Quasi-steady Reaction-diffusion, Quasi-steady Reaction-diffusion Equations